You want the satin on the body or the neck?
If you're just going straight on to the wood, there's a product called Varathane that will do what you want pretty well. You can get it in aerosol cans and you'll need at least four cans for the body. If you want to put it over the neck, you'll want to wipe it first with something to take the oils out.
Otherwise, you might wanna find some aerosol nitrocellulose lacquer, like the stuff sold by stewmac.com and ReRanch. I dunno where to find it in the UK.
The best way to get rid of the dust is by wiping it with a cloth and then with your hands, after they've been washed and dried. That's what I've found. A lot of people say that the oils in your skin can affect the paint, but that's never been a problem for me (maybe I'm not an oily guy). Otherwise, instead of your hands you can buy a tack cloth from a hardware shop.